Zoom Talk: Luca Incurvati (Amsterdam)
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Meta-Inferences and Supervaluationism
Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from being properly axiomatised and from offering a satisfying account of inferential practice. We axiomatise supervaluationist consequence in a multilateral proof theory that keeps track of asserted, rejected and weakly asserted contents. In this proof theory, one can derive supervaluationistically acceptable versions of the classical meta-inferences. The proof theory, moreover, emerges by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. This yields a natural account of our inferential practice. Our axiomatisation brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves validity in the non-normal modal logic NT. Finally, we demonstrate that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. This is joint work with Julian Schlöder.